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MathGroup Archive 2002

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RE: Sum of 1/Primes

  • To: mathgroup at
  • Subject: [mg36973] RE: [mg36910] Sum of 1/Primes
  • From: "DrBob" <drbob at>
  • Date: Thu, 3 Oct 2002 05:33:25 -0400 (EDT)
  • Reply-to: <drbob at>
  • Sender: owner-wri-mathgroup at

No, Euler proved that series divergent in 1737.  It's the usual theorem
used to show that while the primes are sparse, they're not as sparse as
the squares (as the sum of THEIR inverses converges).


-----Original Message-----
From: Matthias.Bode at [mailto:Matthias.Bode at] 
To: mathgroup at
Subject: [mg36973] [mg36910] Sum of 1/Primes

Dear Colleagues,

I calculated:

Sum[1/Prime[n], {n, 15000}] // N

Result: 2.74716

Now I wonder if this sum will converge or keep on growing, albeit very

Best regards,

Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
Tel.: +49(0)69 71 34 53 80
Mobile: +49(0)172 6 74 95 77
Fax: +49(0)69 71 34 95 380
E-mail: matthias.bode at

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